%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL272-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:58:31 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.38s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 33 unt; 0 def)
% Number of atoms : 54 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 24 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 71 ( 8 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rule_1,axiom,
! [VAR_0] :
( ~ axiom(VAR_0)
| theorem(VAR_0) ),
file('theBenchmark.p',rule_1) ).
cnf(c_1,plain,
( ~ axiom(A)
| theorem(A) ),
inference(clausify,[status(thm)],[rule_1]) ).
fof(axiom_1_5,axiom,
! [VAR_0,VAR_1,VAR_2] : axiom(implies(or(VAR_0,or(VAR_1,VAR_2)),or(VAR_1,or(VAR_0,VAR_2)))),
file('theBenchmark.p',axiom_1_5) ).
cnf(c_3,plain,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(clausify,[status(thm)],[axiom_1_5]) ).
fof(axiom_1_4,axiom,
! [VAR_0,VAR_1] : axiom(implies(or(VAR_0,VAR_1),or(VAR_1,VAR_0))),
file('theBenchmark.p',axiom_1_4) ).
cnf(c_4,plain,
axiom(implies(or(A,B),or(B,A))),
inference(clausify,[status(thm)],[axiom_1_4]) ).
fof(axiom_1_3,axiom,
! [VAR_0,VAR_1] : axiom(implies(VAR_0,or(VAR_1,VAR_0))),
file('theBenchmark.p',axiom_1_3) ).
cnf(c_5,plain,
axiom(implies(A,or(B,A))),
inference(clausify,[status(thm)],[axiom_1_3]) ).
fof(axiom_1_2,axiom,
! [VAR_0] : axiom(implies(or(VAR_0,VAR_0),VAR_0)),
file('theBenchmark.p',axiom_1_2) ).
cnf(c_6,plain,
axiom(implies(or(A,A),A)),
inference(clausify,[status(thm)],[axiom_1_2]) ).
cnf(c_7,plain,
theorem(implies(or(A,A),A)),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_8,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_9,plain,
theorem(implies(or(A,B),or(B,A))),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_10,plain,
theorem(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(prove_this,axiom,
~ theorem(equivalent(p,or(p,p))),
file('theBenchmark.p',prove_this) ).
cnf(c_12,plain,
~ theorem(equivalent(p,or(p,p))),
inference(clausify,[status(thm)],[prove_this]) ).
fof(equivalent_defn,axiom,
! [VAR_0,VAR_1] : equivalent(VAR_0,VAR_1) = and(implies(VAR_0,VAR_1),implies(VAR_1,VAR_0)),
file('theBenchmark.p',equivalent_defn) ).
cnf(c_13,plain,
equivalent(A,B) = and(implies(A,B),implies(B,A)),
inference(clausify,[status(thm)],[equivalent_defn]) ).
fof(and_defn,axiom,
! [VAR_0,VAR_1] : and(VAR_0,VAR_1) = not(or(not(VAR_0),not(VAR_1))),
file('theBenchmark.p',and_defn) ).
cnf(c_14,plain,
and(A,B) = not(or(not(A),not(B))),
inference(clausify,[status(thm)],[and_defn]) ).
fof(rule_2,axiom,
! [VAR_0,VAR_1] :
( ~ theorem(VAR_1)
| ~ theorem(implies(VAR_1,VAR_0))
| theorem(VAR_0) ),
file('theBenchmark.p',rule_2) ).
cnf(c_15,plain,
( ~ theorem(B)
| ~ theorem(implies(B,A))
| theorem(A) ),
inference(clausify,[status(thm)],[rule_2]) ).
fof(implies_definition,axiom,
! [VAR_0,VAR_1] : implies(VAR_0,VAR_1) = or(not(VAR_0),VAR_1),
file('theBenchmark.p',implies_definition) ).
cnf(c_16,plain,
implies(A,B) = or(not(A),B),
inference(clausify,[status(thm)],[implies_definition]) ).
cnf(c_81,plain,
~ theorem(and(implies(p,or(p,p)),implies(or(p,p),p))),
inference(paramod,[status(thm)],[c_13,c_12]) ).
cnf(c_82,plain,
~ theorem(and(or(not(p),or(p,p)),implies(or(p,p),p))),
inference(paramod,[status(thm)],[c_16,c_81]) ).
cnf(c_83,plain,
~ theorem(and(or(not(p),or(p,p)),or(not(or(p,p)),p))),
inference(paramod,[status(thm)],[c_16,c_82]) ).
cnf(c_17,plain,
~ theorem(not(or(not(or(not(p),or(p,p))),not(or(not(or(p,p)),p))))),
inference(paramod,[status(thm)],[c_14,c_83]) ).
cnf(c_19,plain,
( ~ theorem(B)
| ~ theorem(or(not(B),A))
| theorem(A) ),
inference(paramod,[status(thm)],[c_16,c_15]) ).
cnf(c_21,plain,
theorem(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(paramod,[status(thm)],[c_16,c_10]) ).
cnf(c_22,plain,
theorem(or(not(or(A,B)),or(B,A))),
inference(paramod,[status(thm)],[c_16,c_9]) ).
cnf(c_23,plain,
theorem(or(not(A),or(B,A))),
inference(paramod,[status(thm)],[c_16,c_8]) ).
cnf(c_24,plain,
theorem(or(not(or(A,A)),A)),
inference(paramod,[status(thm)],[c_16,c_7]) ).
cnf(c_84,plain,
( ~ theorem(or(B,or(A,C)))
| theorem(or(A,or(B,C))) ),
inference(resolve,[status(thm)],[c_19,c_21]) ).
cnf(c_32,plain,
theorem(or(A,or(not(or(B,A)),B))),
inference(resolve,[status(thm)],[c_84,c_22]) ).
cnf(c_85,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),not(or(not(or(not(p),or(p,p))),not(or(not(or(p,p)),p)))))) ),
inference(resolve,[status(thm)],[c_19,c_17]) ).
cnf(c_44,plain,
~ theorem(or(not(or(not(A),or(B,A))),not(or(not(or(not(p),or(p,p))),not(or(not(or(p,p)),p)))))),
inference(resolve,[status(thm)],[c_85,c_23]) ).
cnf(c_86,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(or(not(B),or(C,B))),not(or(not(or(not(p),or(p,p))),not(or(not(or(p,p)),p))))))) ),
inference(resolve,[status(thm)],[c_19,c_44]) ).
cnf(c_69,plain,
~ theorem(or(not(or(not(or(not(p),or(p,p))),not(or(not(or(p,p)),p)))),not(or(not(A),or(B,A))))),
inference(resolve,[status(thm)],[c_86,c_22]) ).
cnf(c_87,plain,
( ~ theorem(A)
| ~ theorem(or(not(A),or(not(or(not(or(not(p),or(p,p))),not(or(not(or(p,p)),p)))),not(or(not(B),or(C,B)))))) ),
inference(resolve,[status(thm)],[c_19,c_69]) ).
cnf(c_79,plain,
~ theorem(or(not(or(not(or(A,A)),A)),or(not(or(not(or(not(p),or(p,p))),not(or(not(or(p,p)),p)))),not(or(not(B),or(C,B)))))),
inference(resolve,[status(thm)],[c_87,c_24]) ).
cnf(c_80,plain,
$false,
inference(resolve,[status(thm)],[c_79,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL272-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n026.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 22:13:10 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.36 % Process 3590562 was started by sandbox2 on n026,
% 0.07/0.36 % Fri Sep 25 22:13:10 2026
% 0.07/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.36
% 0.07/0.36 % From the command line: assign(max_seconds, 300).
% 0.07/0.38
% 0.07/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.38
% 0.07/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.07/0.38 % Length of proof is 25.
% 0.07/0.38 % Level of proof is 6.
% 0.07/0.38 % Maximum clause weight is 33.000.
% 0.07/0.38 % Given clauses 14.
% 0.07/0.38
% 0.07/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------